Tutorial on Shape Optimization Problems

Tuesday, June 7, 2016 - 10:35am - 11:50am
Lind 305
Shawn Walker (Louisiana State University)
1. Quick intro of example shape optimization problems.
2. Review differential geometry for curves/surfaces: parametric surfaces, normal vector, curvature, shape operator, etc.
3. Review surface differential operators: surface gradient/Laplacian, shape operator, integration by parts on surfaces, etc.
4. Intro shape perturbations: material and shape derivatives of functions, shape perturbation of shape functionals, perturbation of the identity, etc.
5. Intro gradient flows: motivate as a way to optimize shape, derive mean curvature flow. Maybe give example of image segmentation if there is time.
6. Application: work through a shape optimization problem with the Stokes equation as a PDE constraint.
MSC Code: